Answer to Question #186080 in Statistics and Probability for mya

Question

A set of data consists of values 10, 12, 14, 16, and 18. Using a

sample size of 3 without replacement, illustrate the Central Limit Theorem by

showing that the histogram of the sampling distribution of the sample mean

resembles a bell curve. complete solution

Answer 1

The sampling distribution of sample means are-

Mean pf sample mean $\bar{x}=\dfrac{126.1}{9}=14.01$

The central limit theorem states that if we have a population with mean $\mu$ and standard deviation $\sigma$ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed.

Histogram of sample mean is-